Weight reduction for mod ℓ Bianchi modular forms

Abstract

Let K be an imaginary quadratic field with class number one and ℓ be a rational prime that splits in K. We prove that mod ℓ, a system of Hecke eigenvalues occurring in the first cohomology group of some congruence subgroup Γ of SL 2 ( O K ) can be realized, up to twist, in the first cohomology with trivial coefficients after increasing the level of Γ by ( ℓ).